Shadow geometry of Kerr MOG naked singularity and analysis of accretion disk luminosity

Abstract Naked singularities are hypothetical astrophysical entities featuring gravitational singularities without event horizons. In this study, we analyze the shadow properties of Kerr modified gravity (Kerr MOG) naked singularities (KMNSs). We show that the KMNS shadow can appear closed or open, or can even vanish, depending on the dimensionless spin parameter a , the modified gravity parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , and the observer’s inclination angle. We identify the critical conditions under which the KMNS shadow develops a gap, a unique feature not present in black hole (BH) shadows. We analyze the properties of a thin accretion disk surrounding a KMNS within the framework of MOG characterized by the parameter $$ \alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> . The study includes a detailed examination of the spacetime geometry and the equations of motion for test particles. In addition, we adopt a simplified model for the disk’s radiative flux, temperature distribution, and spectral luminosity. Our analysis primarily focuses on the flux distribution of the accretion disk around the KMNS with identical mass but varying spin and MOG deformation parameters. This allows us to explore how modifications in rotation and the MOG parameter $$ \alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> influence the radiative properties of the disk. Further, these observational signatures may serve as effective tools for clearly distinguishing KMNSs from standard Kerr naked singularities (KNSs), where the MOG parameter $$ \alpha = 0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> .